Saturday, September 24, 2022

2022-09-30 / 15:00 ~ 16:00

by 최인혁(KAIST)

This series of talks is intended to be a gentle introduction to the random walk theory on infinite groups and hyperbolic spaces. We will touch upon keywords including hyperbolicity, stationary measure, boundaries and limit laws. Those who are interested in geometric group theory or random walks are welcomed to join.

2022-09-27 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

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In real world, people are interested in causality rather than association. For example, pharmaceutical companies want to know effectiveness of their new drugs against diseases. South Korea Government officials are concerned about the effects of recent regulation with respect to an electric car subsidy from United States. Due to this reason, causal inference has been received much attention in decades and it is now a big research field in statistics. In this seminar, I will talk about basic idea and theory in the causal inference. Real data examples will be discussed.

2022-09-27 / 10:00 ~ 11:00

IBS-KAIST 세미나 - 대수기하학: Quasi-F-splittings

by Jakub Witaszek(Princeton University)

What allowed for many developments in algebraic geometry and commutative algebra was a discovery of the notion of a Frobenius splitting, which, briefly speaking, detects how pathological positive characteristic Fano and Calabi-Yau varieties can be. Recently, Yobuko introduced a more general concept, a quasi-F-splitting, which captures much more refined arithmetic invariants. In my talk, I will discuss on-going projects in which we develop the theory of quasi-F-splittings in the context of birational geometry and derive applications, for example, to liftability of singularities. This is joint work with Tatsuro Kawakami, Hiromu Tanaka, Teppei Takamatsu, Fuetaro Yobuko, and Shou Yoshikawa. * Zoom information will not be provided. Please send an email to Jinhyung Park if you are interested in.

2022-09-29 / 11:50 ~ 12:30

대학원생 세미나 - 대학원생 세미나: Kernel methods for radial transformed compositional data with many zeros

by 박준영(KAIST)

Compositional data analysis with a high proportion of zeros has gained increasing popularity, especially in chemometrics and human gut microbiomes research. Statistical analyses of this type of data are typically carried out via a log-ratio transformation after replacing zeros with small positive values. We should note, however, that this procedure is geometrically improper, as it causes anomalous distortions through the transformation. We propose a radial transformation that does not require zero substitutions and more importantly results in essential equivalence between domains before and after the transformation. We show that a rich class of kernels on hyperspheres can successfully define a kernel embedding for compositional data based on this equivalence. The applicability of the proposed approach is demonstrated with kernel principal component analysis.

2022-09-27 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Ramsey Theory for Diffsequences

by Alexander Clifton(IBS 이산수학그룹)

Van der Waerden's theorem states that any coloring of $\mathbb{N}$ with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van der Waerden number $W(r,k)$ which is the smallest $n$ such that any $r$-coloring of $\{1,2,\cdots,n\}$ guarantees the presence of a monochromatic arithmetic progression of length $k$. It is natural to ask what other arithmetic structures exhibit van der Waerden-type results. One notion, introduced by Landman and Robertson, is that of a $D$-diffsequence, which is an increasing sequence $a_1

2022-09-29 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

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We consider a deep generative model for nonparametric distribution estimation problems. The true data-generating distribution is assumed to possess a certain low-dimensional structure. Under this assumption, we study convergence rates of estimators obtained by likelihood approaches and generative adversarial networks (GAN). The convergence rate depends only on the noise level, intrinsic dimension and smoothness of the underlying structure. The true distribution may or may not possess the Lebesgue density, depending on the underlying structure. For the singular case (no Lebesgue density), the convergence rate of GAN is strictly better than that of the likelihood approaches. Our lower bound of the minimax optimal rates shows that the convergence rate of GAN is close to the optimal rate. If the true distribution allows a smooth Lebesgue density, an estimator obtained by a likelihood approach achieves the minimax optimal rate.

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